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Rising Algebra 1 – Summer Math Packet
Student Information Page
We’re so proud of you for taking the time to work on math over the
summer!
Here are some helpful hints for success:
 It’s ok to have parents and other adults help you!
 Find a quiet workspace where you can get organized and stay focused.
 Pay close attention to the examples and vocabulary.
 Choose a unit that you like, and work through it completely before moving on
to another unit.
o Try to complete at least 1 worksheet per day.
o Complete all of the problems on each worksheet.
o Don’t forget to number your problems and show all work
 Calculators may ONLY be used when you see this symbol:
 Remember to do a little work each week. DO NOT wait until the week before
school starts to complete your packet!
 The packet should be returned to your math teacher during the first day of
school.
Have fun & we’ll see you in July 29th!
1
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Algebra, Patterns, and Functions
Objective: Identify Equivalent Equations
Example:
Which equation is equivalent to 3x + 2 = 8?
A) x + 4x = 5
B) x + 2 = 6
C) 6x + 5 = 11
D) 4x – 3 = 5
STRATEGY: Solve the given equation and each of the equation choices and compare the solutions.
Step 1: Solve the given equation. 3x + 2 = 8
Subtract 2 from both sides
1
3x = 6
Divide both sides by 3 (or multiply by )
3
x=2
An equivalent equation MUST have a solution of 2.
Step 2: Solve Choice A.
x + 4x = 5
5x = 5
x=1
Step 3: Solve Choice B.
Step 4: Solve Choice C.
6x + 5 = 11
Step 5: Solve Choice D.
6x = 6
x=1
SOLUTION: The equation that is equivalent to 3x + 2 = 8 is 4x – 3 = 5, Choice D.
1.) Solve: 7x + 3 = 24
h
2.) Solve: 7 + = 5
3
3.) Which of the following equations is equivalent to
30 = 5d + 6 – 2d ?
A)
B)
C)
D)
x+2=6
x =4
4x – 3 = 5
4x = 8
x=2
4.) Which of the following equations is equivalent to
6 = 2x + 5 ?
30 = 7d + 6
10 + 20 = 3d – 6
35 + 5 = 3d + 6
30 = 3d + 6
A) 4x – 6 = 6x + 5
B) 8x = 6x + 5
C) 8x + 12 = 12x + 10
6.) Which of the following equations is not equivalent to
the equation below?
8x + 5x – 5 = 12 + 9
5.) Are the two equations given equivalent?
50 = 6 + –11c
6c – 14 + 5c + 8 = –50
2
A) x = 2
B) 13x – 5 = 21
C) 13x = 26
D) 13x = 21
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Geometry
Objective: Identify and describe relationships between angles formed when parallel lines are cut by a transversal.
Example:
 Interior Angles – lie inside the parallel lines
- Angles 3, 4, 5, 6 are INTERIOR angles
 Exterior Angles – lie outside the parallel lines
2
- Angles 1, 2, 7, 8 are EXTERIOR angles)
1
 Vertical Angles – angles opposite one another and are EQUAL
4
3
- 1 & 4, 2 & 3, 5 & 8, 6 & 7 are Vertical Angles.
 Alternate Interior Angles
6
– on opposite sides of the transversal and inside the parallel lines
5
8
- Alternate Interior Angles are EQUAL.
7
- 3 & 6…...4 & 5 are Alternate Interior angles
 Alternate Exterior Angles
– on opposite sides of the transversal and outside the parallel lines
- Alternate Exterior Angles are EQUAL.
- 1 & 8 …………2 & 7 are Alternate Exterior angles
 Corresponding Angles
– in the same position on the parallel lines in relation to the transversal
- Corresponding Angles are EQUAL.
- 1 & 5, 2 & 6, 3 & 7, 4 & 8 are Corresponding Angles
7.)
8.)
t
l
t
l
E
l || m
m
120
F
m
Identify the geometric relationship shown above.
l || m
x
In the figure above, line l and m are parallel. What is the
measure of x? What is the relationship between the two
shown?
9.) Identify 2 alternate Interior Angles.
1
l
3
5
m
7
2
4
l || m
6
10.) What type of angles are 2 & 7?
8
In the figure above, the m  4 = 103. Determine the
measure of m  5.
A) 113
B) 77
C) 107
D) 103
12.) In the figure above, if the m  7 = 58. Determine the
measure of m  6.
11.)
3
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Geometry
Objective: Use the Pythagorean Theorem
Examples:
 If a triangle is a RIGHT triangle, then the square of the length
of the hypotenuse is equal to the sum of the squares of the
lengths of the legs.

a2 + b2 = c2
legs
a2
c
16
cm
30 cm
b2
+ =
162 + 302 = c2
256 + 900 = c2
1156 = c2
√1156 = √c2
34 = c
c2
c = 22
a
c
a
14 cm
hypotenuse
b
a2 + b2 = c2
a2 + 142 = 222
a2 + 196 = 484
a2 + 196 – 196 = 484 – 196
a2 = 288
√a2 = √288
a = 16.97056275
a = 16.97  17
You may use a calculator on this page to complete # 1- 6.
13.) Determine the length of the missing side.
14.) Determine the length of the missing side.
18
cm
c
c
15
cm
24 cm
20 cm
15.) If c is the measure of the hypotenuse, Determine the 16.) Determine the length of the missing side. Round to
missing measure. Round to the nearest tenth if necessary. the nearest tenth if necessary.
a = 10, b = ?, c = 18
c = 20
a
8 ft
17.) Kristen is flying a kite. The length of the kite string is
55 feet and she is positioned 33 feet away from beneath
the kite. About how high is the kite?
17.) Brandon rides his bike 9 miles south and 12 miles
west. How far is he from the starting point of his bike ride?
(Hint: You may want to draw a picture to help you set up
the problem.)
(Hint: You may want to draw a picture to help you)
A) 47 ft
B) 45 ft
C) 44 ft
D) 40 ft
4
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Geometry
Objective: Determine whether 3 given side lengths form a right triangle
Examples:
 If a triangle is a RIGHT triangle, then the square of the length
of the hypotenuse is equal to the sum of the squares of the
lengths of the legs.
 a2 + b2 = c2
34 ft
hypotenuse
b
legs
16
ft
c
a
42 in
21
in
30 ft
29 in
a2 + b2 = c2
162 + 302 = 342
256 + 900 = 1156
1156 = 1156
a2 + b2 = c2
+ 292 = 422
441 + 841 = 1764
1282 = 1764
212
Yes, this is a right triangle!
NO, this is not a right triangle!
You may use a calculator to solve # 1 – 6.
18.) The lengths of three sides of a triangle are given.
Determine whether each triangle is a right triangle.
19.) The lengths of three sides of a triangle are given.
Determine whether each triangle is a right triangle.
a = 5, b = 8, c = 9
a = 16, b = 30, c = 34
20.) The lengths of three sides of a triangle are given.
Determine whether each triangle is a right triangle.
21.) The lengths of three sides of a triangle are given.
Determine whether each triangle is a right triangle.
a = 24, b = 28, c = 32
6 in, 7 in, 12 in
22.) The lengths of three sides of a triangle are given.
Determine whether each triangle is a right triangle.
23.) The size of a television set is determined by the length
of the diagonal of the screen. If the screen is 27 inches
long, 36 high and the diagonal is 45 inches, is this a true
measurement for the television set?
9 m, 12m, 15m
5
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Geometry
Objective: Draw quadrilaterals given their whole number dimensions in in/cm of angle measurements
Examples:
 A closed figure with 4 sides & 4 vertices. Such as Parallelogram, Rectangle, Square, Rhombus, etc.
 Can be separated into 2 triangles => Measures in a triangle = 180o
 Sum of measures of the angles in a Quadrilateral = 360o
B
Look at the quadrilateral:
A + B + C + D = 360o
3x + 4x + 90 + 130 = 360
7x + 220 = 360
7x + 220 – 220 = 360 – 220
7x = 140
7x ÷ 7 = 140 ÷ 7
x = 20
4x
A
Value of x = 20 … So, A = 3x
A = 3(20)
A = 60o
3x
B = 4x
B = 4(20)
B = 80o
D
**Note: All figures are NOT drawn to scale.
24.) Determine the measure of the missing angle.
25.) Determine the measure of the missing angles.
C
B
95
105
A
C
130
B
55
140
x C
A
D
26.) Tell whether each statement is sometimes, always, or
never true.
2x
40
x
27.) Determine the value of x. Then determine the missing
angle measures.
105 130
A rhombus is a square.
____________________
A square is a parallelogram. ____________________
A parallelogram is a square. ____________________
A parallelogram is a trapezoid. ____________________
A square is a quadrilateral.
____________________
3x
28.) Determine the value of x. Then determine the
missing angle measures.
2x
x
D
2x
27.) Determine the value of x. Then determine the
missing angle measures.
8x
60
60
120
6
2x
10x
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Measurement
Objective: Estimate and determine the circumference or area of a circle
Examples:
 Circumference – Distance around the outside of a circle
d
C = πd or C = 2πr

Area – amount of space inside the circle
A = πr2
7
km
Where
d = diameter
r = radius
r
Notice:
 In the example to the left, the radius is given.
In the example to the right, the diameter is given. 
Area:
Area:
Circumference:
A = π r2
A = 3.14 • 72
A =153.86 km
30
km
Circumference:
(need radius – cut diameter in half)
A = π r2
A = 3.14 • 152
A =706.9 km
C = 2πr
C = 2 • 3.14 • 7
C = 44 km
Remember:
r2 = r • r
π = 3.14
d = 2r
r=½d
C = πd
C = 3.14 • 30
C = 94.2 km
You may use a calculator to solve #1 – 6. Round all answers to the nearest hundredth if necessary.
28.) Determine the area of the circle.
29.) Determine the circumference of the circle.
r = 3 cm
d=7m
30.) Estimate the area the circle. Round given values to
the nearest whole number.
31.) Estimate the circumference the circle. Round given
values to the nearest whole number.
3.87
mi.
9.87
mi.
32.) You are making a pie for Pi Day (3/14). You need to
determine the area of your pie as part of your assignment.
You know that your pie has a diameter of 8 inches. What
is the area of your pie?
33.) You are on a picnic with your friends at the beach this
summer. Your friend challenges you to determine the
circumference of a plate. You figure out that the radius is
4.5 inches. What is the circumference of the plate?
7
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Measurement
Objective: Estimate and determine area of composite figures
Examples:
Parallelogram
A = bh
Triangle
A = ½ bh
h
h
b
Steps:
Trapezoid
b2
A = ½ h (b1 + b2)
h
b
b1
1. Split figure into smaller known figures
2. Determine area of each of the smaller figures & add all areas together
22 mm
2 ft
20 mm
6 ft
10 mm
Determine the areas:
Triangle:
A = ½ bh
A = ½•17•20
A = 17 • 10 = 170
8 ft
Determine the area of both shapes:
Rectangle:
Triangle: A = ½ bh
A = bh
A=½•8•6
A = 6 • 2 = 12
A = ½ • 48 = 24
Trapezoid:
A = ½ h (b1+b2)
A = ½•17•(10 + 22)
A = ½ •17• 32
A = 17 • 16 = 272
Add Areas Together:
Add Areas: 12 + 24 = 36 ft2
You may use a calculator to solve #1 – 6.
34.) Estimate the area of this figure.
7 ft.
17 mm
170 + 272 = 442 mm2
35.) Determine the area of this figure.
5m
5.8
ft.
8m
ft.2
ft.2
a) 54
b) 65
c) 170
36.) Determine the area of the figure.
4.3 ft.
d) 70 ft.2
4m
37.) Determine the area of the figure.
4 ft
5m
7 ft
8 ft
2 ft
8m
5m
38.) You are building a garden. The following is the shape
you have decided on. Determine the area of the figure in
order for you to buy mulch. Round your answer to the
nearest whole unit. Use  = 3.14.
14 m
6m
10 m
ft.2
39.) Susan is re-finishing her kitchen floor. The
dimensions of her kitchen floor are shown below:
24 feet
6 feet
6m
10 m
4 feet
15 feet
(NOTE: The
figure is not
drawn to
6 feet
scale.)
What is the area, in square feet, of Susan’s kitchen floor?
a) 250 ft2
b) 266 ft2
c) 298 ft2 d) 302 ft2
h=
8m
8
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Measurement
Objective: Estimate and determine the volume of a cylinder
Examples:
 Amount a 3-D figure will hold
 Always cubed. For Example: cm3 or cubic centimeters
 FORMULA: Generalized: V = Bh where B = area of the base and h = height
Volume of Cylinders: The volume V of a cylinder with radius r is the area of the base, πr2, times the height h, or
V = π r2 h
r = 2.2 ft
h = 4 ft
V = π r2 h
V = 3.14• 2.22 • 4
V = 3.14 • 4.84 • 4
V = 15.1976 • 4
V = 60.7904 = 60.8 ft3
d = 20 ft
h = 5 ft
V = π r2 h
V = 3.14• 102 • 5
V = 3.14 • 100 • 5
V = 314 • 5
V = 1570 = 1570 ft3
*Note:
d = 20 THEREFORE r = 10
102 = 10 x 10 = 100
*Note:
2.22 = 2.2 x 2.2 = 4.84
You may use a calculator to solve # 1 – 6. Round to the nearest hundredth if necessary.
40.) Estimate the volume of this cylinder.
41.) Determine the volume of this cylinder.
4 yd.
5m
8
yd.
11 m
A) 384 yd.
B) 790 yd. C) 401 yd.
D) 785 yd.
42.) Determine the volume of this cylinder.
12 mm
3
3
3
3
43.) Determine the volume of this cylinder.
18 cm
9 cm
7
mm
44.) A water tank is in the shape of a cylinder that has a
height of 75 meters and a diameter of 20 meters.
Determine the volume of this cylinder.
45.) Your Science teacher is teaching your class about
Kaleidoscopes and how to build them. Your Kaleidoscope
has a radius of 2 inches and a height of 9 in. What is the
volume of your Kaleidoscope?
9
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Measurement
Objective: Use proportions, scale drawings, or rates to solve measurement problems - A
Examples:


Scale drawings and scale models can show objects that may be very big, or very small, or very complex. Common examples of scale
drawings and scale models are maps, architects’ drawings, and models of homes and buildings.
In all cases a numerical scale is used to compute the actual dimensions. A scale is a ratio – the ratio between the dimensions of the
drawing and the actual dimensions of the object.
Proportions are useful in solving a variety of problems. Be sure to set up the proportion according to the labels!


On a map, Andy measured the distance between Baltimore and Hagerstown. It is 9 cm. The scale on the map shows 4 cm = 30 miles.
What is the approximate distance from Baltimore to Hagerstown? STRATEGY: Write a proportion and solve it.
Step 1: Use the scale to set up a proportion.
Step 2: Solve the proportion by cross-multiplying.
CM
4 9


MI 30 n
4 x n = 9 x 30
4n = 270
(Divide both sides by 4)
n = 67.5 miles
SOLUTION: The approximate distance from Baltimore to Hagerstown is 68 miles.
Look at this scale drawing. How many meters long is the actual race car?
STRATEGY: Set up a proportion and solve it.
cm
1
cm
5
and for the car.


m 1.5
m ?m
1
5
Step 3: Set up the proportion & solve it for m.

1.5 m
1m = 5 x 1.5
m = 7.5 meters
Step 1: Set up the scale as a ratio.
SOLUTION: The actual race car is 7.5 meters long.
46.) Use proportions to solve.
47.) The distance on a map is 4.25 inches. The map
scale is 1 inch = 6 miles. What is the actual distance?
inches 1 4.25
 
miles
6
n
6 n

9 12
48.) On an architectural drawing, the scale is 0.25 inch=5
feet. Determine the actual length of a room that has a
drawing distance of 2 inches.
49.) Solve the proportion:
inches 0.25 n


feet
2
48
inches 0.25 2


feet
5
n
50.) A girl who is 4 feet tall casts a shadow of 3 feet. If a
flagpole is 20 feet high, what is the length of the shadow of
the flagpole?
5 cm
SCALE: 1 cm = 1.5 m
51.) On a map, the key indicates that 1 cm = 3.5 meters.
A road is shown on this map that runs for 30 cm. How
long is this road?
10
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Measurement
Objective: Use proportions, scale drawings, or rates to solve measurement problems - B
Examples:

A RATE is a fixed ratio between two quantities of different units, such as miles and hours, dollars and hours, points and games. If the
second number of a rate is 1 then the rate is called a UNIT RATE. UNIT RATE examples: 60 miles per hour and $15 per hour
Last week Mike worked 30 hours and earned $240. What was his rate of pay?
STRATEGY: Divide the total earned by the number of hours.
Step 1: How much money did Mike earn?
$240
Step 2: How many hours did he work?
30 hours
Step 3: Determine the rate of pay.
amount of $
240

 $8 per hour
# of hours worked 30
Divide the amount of money earned by the number of hours.
SOLUTION: Mike earned $8 per hour. (note: this is a unit rate)
The unit price of a can of tuna fish at the GHK Supermarket is $2.43. How much will 7 cans cost?
STRATEGY: Use the definition of unit price.
Step 1: Unit price means the price of one unit or the price of one can of tuna fish. $2.43
Step 2: Multiply.
2.43 x 7 = $17.01
SOLUTION: Seven cans of tuna fish cost $17.01
52.) If you travel 500 km in 20 hours, how many km do
you travel per hour?
53.) A 2.6-kg bag of cherries for $4.84. How much per
kg.
________ per kg
54.) There are 1962 calories for 6 servings of pie. How
many calories per serving?
55.) An international phone call costs $8.72 for 27
minutes. How many cents per minute does an
international phone call cost?
________ calories per serving
________ cents per minute
56.) You were hired for the summer to mow your
neighbor’s lawn. You earned a total of $372 and worked a
total of 12 days. How much did you earn per day?
57.) Sheryl swims 5 laps in 15 minutes. At this same rate,
how many laps will she swim in 30 minutes?
11
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Statistics
Objective: Interpret circle graphs
Examples:
Textbook Section: NONE
Playing
Computer Watching TV
Other
Games
15%
5%
A Circle Graph is useful when you want to compare parts of a whole.
This circle graph shows the favorite pastimes of a group of 8th graders.
STRATEGY: Use the data in the circle graph.
10%
Talking on the
Phone 25%
Reading 20%
Playing Sports
25%
Favorite Pastimes
1.) Which two activities were equally popular?
Step 1: Look for activities with the same percent.
Playing Sports and Talking on the Phone are each 25%
SOLUTION: Playing Sports and Talking on the Phone were equally popular.
2.) What percent of students chose Reading or Watching TV?
Step 1: Determine the sum of the percents for Reading and Watching TV.
SOLUTION: 35% of the students chose Reading or Watching TV.
20% + 15% = 35%
3.) If 320 students were surveyed, how many would have chosen playing computer games?
Step 1: Determine the % for playing computer games. Change to a decimal. 10% = 0.10
Step 2: Multiply by the total.
320 x 0.10 = 32.0
SOLUTION: 32 students chose playing computer games as their favorite pastime.
Use the following circle graph to answer questions 1 – 6.
Bus Fare
25%
Michelle’s Expenses Last Month
Snacks 40%
Phone Calls
10%
Video 25%
58.) What percent did Michelle spend on Snacks and Bus
Fare?
59.) Which 3 expenses make up 90% of Michelle’s
budget?
60.) If Michelle received $80 last month for allowance,
how much did she spend on Videos?
61.) How much would Michelle have spent on snacks and
bus fare if her allowance was $125?
62.) How much more did Michelle spend on Video’s than
on phone calls if she received an allowance of $95?
63.) Michelle’s allowance for the month was $100,
however she did some extra work for her grandparents
and earned $35 more dollars to add to her total allowance.
Based on her total, how much would Michelle spend on
Bus Fare and Phone calls?
12
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Statistics
Objective: Interpret tables
Examples:


A table contains numerical information or data that is organized. The data is arranged in columns, each providing a
specific type of information.
You can use the data in a table to solve problems.
How many more computers are in Room 108 than in Room 215?
Computers in Computer Labs at Blake Middle School
Classroom
PC
Macintosh
104
18
8
108
12
6
207
5
11
215
8
7
302
4
9
STRATEGY: Add the numbers in the two different rows and subtract the sums.
Step 1: Determine the row for Room 108 & add the numbers
12 + 6 = 18
Step 2: Determine the row for Room 215 & add the numbers
8 + 7= 15
Step 3: Subtract the sum for Room 215 from the sum for Room 108.
18 – 15 = 3
SOLUTION: There are 3 more computers in Room 108.
Maryland State Parks
Park
Assateague Island
Janes Island
Martinak
Pocomoke River
Tuckahoe
# of Campsites
350
104
63
223
51
Area in Acres
756
3,147
107
94
3,498
Use the Maryland State Parks Table to your left to
answer questions 1 & 2.
64.) How much larger is Janes Island State Park than
Pocomoke River State Park?
65.) Which two Islands total more than 4,000 acres but less
than 5,000 acres? What is their total combined acreage?
This table shows how much money five teams raised during a two-day car wash. Use the table to answer questions # 3 – 6.
CAR WASH FUND-RAISER
Team
Blue
Yellow
Red
Green
Purple
Saturday
$65
$45
$40
$25
$55
Sunday
$35
$40
$35
$25
$40
66.) Which team raised the largest amount of money?
67.) What was the total amount of money raised on Saturday?
68.) What fraction of the total amount collected on Sunday did
the Red team collect?
69.) What percent, of the total amount collected on Saturday
did the Purple team collect? Round your answer to the nearest
tenth
13
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Probability
Objective: Express the probability of an event as a fraction, a decimal, or a percent
Examples:
Probability is a way to measure the chance that an event will occur. You can use this to determine the probability, P, of an event.
P = number of favorable outcomes
Number of possible outcomes
Probability can be expressed as a FRACTION, DECIMAL, or PERCENT.
A jar contains 10 purple, 3 orange, and 12 blue marbles. A marble is drawn at random.
Determine the probability that you will pick a purple marble. Express your answer in a fraction, decimal, and %.
Step 1 – Determine the total # of marbles. 10 + 3 + 12 = 25
Step 2 – Determine the probability of picking a purple marble. P(purple) = number of purple = 10 ÷ 5 = 2
Total marbles
Step 3 – Simplify the fraction.
25 ÷ 5 = 5
Step 4 – Convert Fraction to a Decimal – Divide. 2 ÷ 5 = 0.4
Step 5 – Convert Decimal to a % - Move decimal 2 places to the right. 0.4 = 40%
For Questions # 1 – 6, Determine the probability for the following situation. Express your answer in Fraction,
Decimal, and % forms.
A jar contains 15 orange, 14 white, 10 pink, 2 green, and 4 blue marbles. A marble is drawn at random.
70.) P (orange) =
71.) P (black) =
72.) P (not blue) =
73.) P (not pink) =
74.) P (all colors) =
75.) P (pink or orange) =
14
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Probability
Objective: Describe the difference between independent and dependent events
Examples:
Probability is a way to measure the chance that an event will occur. You can use this to determine the probability, P, of an event.
P = number of favorable outcomes
Number of possible outcomes
Two events are INDEPENDENT when the outcome of one event has no effect on the outcome of another event. For example:
 Event: tossing a coin and getting tails OR Event: tossing a number cube and getting a number less than 5
When determining the probability of two independent events, multiply the probabilities of the two events to get the total probability.
This is called the multiplication rule.
Determine the probability of tossing a coin and getting tails and tossing a number cube and getting a number less than 5.
STRATEGY: Find the probability of each even and apply the multiplication rule.
Step 1: Determine the probability of each event.
Tossing the coin:
Tossing the number cube:
Probability of tails =
1
2
Probability of a # < 5 =
Step 2: Apply the multiplication rule:
SOLUTION: The probability is
4 2

6 3
1 2 2 1
x  
2 3 6 3
1
.
3
Two events are DEPENDENT when the outcome of one event is affected by the outcome of the other. For Example: You draw a
yellow marble out of a bag of marbles and do NOT replace the marble before drawing a second marble. If you started with 20
marbles, you no longer have 20 – you now have 19. This situation is DEPENDENT on what happened during the first draw.
76.) Describe the difference between Independent &
Dependent Events. Give an example of each (Do not use the
above examples.
77.) Tell whether each situation is INDEPENDENT or
DEPENDENT.
A) Picking a cookie from the cookie jar, eating it, then
choosing another cookie.
B) Toss a coin and spin a colored spinner
C) Picking colored marble and then rolling a die
78.) You flip a coin and toss a 1-6 number cube. Determine
79.) Jack heard the weather forecast on TV: the probability of
the probability that you will roll anything but a 3 and will not get
tails.
rain today is 20% and the probability of rain tomorrow is 50%.
What is the probability that it will rain on both days?
P(not tails and not a 3) =
80.) A bag contains 2 Snickers, 3 Milky Way, and 5 Heath
81.) You roll a number cube numbered from 1 to 6. You then
snack bars. Bailey reaches in the bag and randomly takes two
snack bars, one after the other. She wants to know the
probability that she will choose a Snickers bar and then a Milky
Way bar.
spin a spinner with 3 sections each with a different color. The
spinner has the colors orange, gray, and pink. Determine the
probability shown below:
INDEPENDENT
OR
DEPENDENT
P(2, 4, 1, 5, or 3 and orange) =
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Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Probability
Objective: Determine the probability that a second event is dependent upon a first event of equally likely outcomes and
express the probability as a fraction, decimal, or percent
Examples:
 Remember: Two events are DEPENDENT when the outcome of one event is affected by the
outcome of the other.
A bag contains 3 green, 3 blue, and 3 yellow marbles. What is the probability of drawing a blue marble followed by a yellow
marble in that order when you draw two marbles from the bag without returning the first marble to the bag?
STRATEGY: Use the multiplication rule.
Step 1: Determine the probability of getting blue as the first marble.
3 of 9 marbles are blue =
Step 2: Determine the probability of getting yellow as the second marble.
After the first selection, 8 marbles remain in the bag.
3 of the marbles are yellow =
3 1

9 3
3
8
1 3 3 1
x 

3 8 24 8
Step 3: Apply the multiplication rule.
SOLUTION: The probability of getting blue and then yellow without returning the first marble to the bag is
You can express the probability as a fraction, decimal, or percent:
1
.
8
1
 1  8  0.125  12.5%
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82.) A deck of cards has 3 blue, 4 black, and 6 purple cards.
83.) There are 6 red, 2 yellow, 6 black, and 5 blue marbles in a
You pick 2 cards from the deck. Cards are not returned to the
deck after they are picked. Express the probability as a
simplified fraction.
hat. You pick 2 marbles from the hat. Marbles are not returned
after they have been drawn. Express the probability as a %.
Round to the nearest tenth.
P(two blue cards in a row) =
P(the first marble is red and the second marble is black)
84.) Mike has 25 red tiles, 10 green tiles, and 15 blue tiles in a
85.) A standard deck of cards has 13 hearts, 13 diamonds, 13
paper bag. If he chooses a tile at random, does not return it to
the bag, and then chooses a second tile, what is the probability
that the two tiles will be green and blue in that order? Express
your answer in a decimal, rounded to the nearest hundredth.
clubs, and 13 spades. Juan picks one card from the deck and
gets a heart and does not replace it in the deck of cards.
Determine the probability that Juan will now pick a club from the
deck. Express your answer as a fraction.
86.) A bag contains 3 green, 3 blue, and 3 yellow marbles.
87.) Jason has 4 quarters, 3 dimes, and 3 nickels in his pocket.
You reach into the bag and pull out a blue marble and do not
replace it. Determine the probability that you will now pick out a
yellow marble. Express your answer as a decimal.
Jason reaches into his pocket and pulls out a dime and does not
replace it. Determine the probability that he will now pull out a
nickel. Express your answer as a percent. Round your answer
to the nearest tenth of a percent
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Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Number Relationships and Computation
Objective: Estimate the square roots of whole numbers
Examples:
A.)

A Perfect Square is the square of a whole number.

A square root of a number is one of two equal factors of the number.

Every positive number has a positive square root and a negative square root.

The square root of a negative number such as -25, is not real because the square of a number is never
negative.
144
Since 122 = 144, then 144 = 12
B.) - 49
Since 72 = 49, then
C.) ± 4
Since 22 = 4, then ± 4 = ± 2
88.) Determine the square root:
49 = -7
 100
D.)
34 Determine a perfect square closest to 34.
5x5 = 25
34
6x6 = 36  this is closest to 34
So we know that the answer is going to be less than
6 but not by much. Estimate: 5.8
Use a calculator to check…round to the nearest tenth
5.830951895  5.8
89.) Estimate the square root:
47
(Round to the nearest tenth)
Check your estimate with a calculator.
90.) Determine the square root:  81
91.) Estimate the square root:  310
(Round to the nearest tenth)
Check your estimate with a calculator.
92.) A square tarpaulin covering a softball field has an
area of 121 m2. What is the length of one side of the
tarpaulin?
93.) If x2 = 76, estimate the value of x to the nearest whole
number? Do not use a calculator.
(Hint: Determine the square root of 121)
17
Rising Algebra 1 – Summer Math Packet
Unit: Knowledge of Number Relationships and Computation
Objective: Solve problems using proportional reasoning
Examples:
 Proportions are useful in solving a variety of problems.
 Be sure to set up the proportion according to the labels! Use this to help you set up the proportion.
 In a PERCENT PROPORTION, one of the numbers, called the PART is being compared to the whole quantity
called the BASE. The other ratio is the %, written as a fraction, whose base is 100.
PERCENT PROPORTION:
%
part
100 = whole
A) Twelve is what % of 16?
Part
Whole
12
16 =
%
100
Cross multiply
Divide to get n
By itself
B) What # is 1.4% of 15?
Part
n
1.4
Whole 15 = 100
12 x 100 = 16 x n%
1200 = 16n
16
16
75 = n
n x 100 = 15 x 1.4
100n = 21
100
100
So 12 is 75% of 16.
n = 0.21
C) 225 is 36% of what #?
Part
Whole
225
n
D) If 6 out of 8 students wore shorts to school, how
many students are in the school if there were 630
students wearing shorts?
36
100
Part
Whole
=
n x 36 = 225 x 100
36n = 22500
36
36
630
n
8 x 630 = 6 n
5040 = 6 n
6
6
n = 625
94.) Use proportions to solve.
6
8
n = 840 students
95.) Use proportions to solve.
What percent of 60 is 15?
75 is 20% of what number?
96.) If 5 out of 10 people prefer Trident gum. How many
people out of 20 would you expect to like Trident?
97.) 300 students were surveyed. 50 of them liked
pepperoni pizza the best. How many students would you
expect to like pepperoni pizza if you asked 600 students?
98.) 20% of the M&M’s in your bag are the color blue. If
there are 50 M&M’s total, how many are blue?
99.) You earned 20 points on a test out of 50. What was
your percent on the test?
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